A fundamental issue in communications is the efficiency and reliability with which data is transmitted on channels. As future-generation multimedia mobile communications require high-speed communication systems capable of transmitting a variety of information including video and wireless data beyond the voice-focused service, it is very significant to increase system efficiency by using a channel coding method suitable for a system.
Generally, a transmission signal in a wireless channel environment of a mobile communication system inevitably experiences loss due to several factors such as multipath interference, shadowing, wave attenuation, time-variant noise, and fading. The information loss causes a severe distortion to the transmission signal, degrading an entire system performance. In order to reduce the information loss, many error control techniques are usually utilized to increase system reliability. A basic error control technique is to use an error correction code.
Additionally, multipath fading is relieved by diversity techniques in the wireless communication system. The diversity techniques are time diversity, frequency diversity, and antenna diversity.
Antenna diversity uses multiple antenna and is further branched into receive (Rx) antenna diversity using a plurality of Rx antenna diversity using a plurality of Rx antennas, Tx antenna diversity using a plurality if Tx antennas, and multiple-input multiple-output (MIMO) using a plurality of Tx antennas and a plurality of Rx antennas.
MIMO is a special case of space-time coding (STC) that extends coding of the time domain to the space domain by transmission of a signal encoded in a predetermined coding method through a plurality of Tx antennas, with the intentions of achieving a lower error rate.
Vahid Tarokh et. al. proposed space-time block coding (STBC) as one of methods of efficiently applying antenna diversity (see “Space-Time Block Coding from Orthogonal Designs”, IEEE Trans. On Info., Theory, Vol. 45, pp. 1456-1467, July 1999). The Tarokh STBC scheme is an extension of the transmit antenna diversity scheme of S. M. Alamouti (see, “A Simple Transmit Diversity Technique for Wireless Communications”, IEEE Journal on Selected Area in Communications, Vol. 16, pp. 1451-1458, October 1988), for two or more Tx antennas.
A STFBC scheme is proposed as another method of efficiently applying the antenna diversity scheme. FIG. 1 is a block diagram of a transmitter in a mobile communication system using such STFBC scheme. As illustrated FIG. 1, a transmitter includes a modulator 100, a serial-to-parallel (S/P) converter 102, an STBC coder (Encoder) 108, and three Tx antennas 106.
Referring to FIG. 1, a transmission scheme of the transmitter is described as follows. A modulator 100 modulates input information data (or coded data) in a predetermined modulation scheme. The modulation scheme can be one of binary phase shift keying (BPSK), quadrature phase shift keying (QPSK), quadrature amplitude modulation (QAM), pulse amplitude modulation (PAM), and phase shift keying (PSK).
The S/P converter 102 parallelizes serial modulation symbols received from the modulator 100, s1, s2, s3, s4. The SFTBC coder 108 encodes four data from the S/P converter 102 using a scheme defined by Equation (1), in order to achieve full diversity.si=xiejθ  (1)
where 1≦i≦4, Xi is a modulated symbol value, Si is a value rotated by ⊖. A re-combiner 106 receives the pre-coded symbol Si and groups the real and imaginary parts of the pre-coded symbol sequence by twos in an interleaving scheme, thereby generating symbol vectors. That is, the re-combiner recombines input pre-coded symbols, thereby generating {tilde over (s)}i as Equation (2).{tilde over (s)}1=s1I+js3Q;{tilde over (s)}2=s2I+js4Q;{tilde over (s)}3=s3I+js1Q;{tilde over (s)}4=s4I+js2Q;{tilde over (s)}5=s5I+js7Q where si=siI+jsiQ.   (2)where I represents real part, Q represents imaginary part, and j represents complex number.
The four recombined symbols are STFBC coded and transmitted through the three transmit antennas. A coding matrix used to generate the combinations is expressed as shown in Equation (3).
                    A        =                  [                                                                                          s                    ~                                    1                                                                              -                                                            s                      ~                                        2                    *                                                                              0                                            0                                                                                                          s                    ~                                    2                                                                                                  s                    ~                                    1                  *                                                                                                  s                    ~                                    3                                                                              -                                                            s                      ~                                        4                    *                                                                                                      0                                            0                                                                                  s                    ~                                    4                                                                              -                                      s                    3                    *                                                                                ]                                    (        3        )            where, {tilde over (s)}1˜{tilde over (s)}4 are symbols passed through the pre-coder 104 and the re-combiner 106. The present method was proposed by Indian Sundar Rajan professor group. However, as Equation (1), it is obvious not to only for configuring STFBC coder. Equation (3) is used to arrange properly for grouping four input data by twos using Alamouti scheme and enabling STFBC coder configured by the Alamouti scheme with the two transmit antennas to transmit them through three antennas.
The Alamouti scheme for the two transmit antennas can be configured using one of matrixes of Equation (4) for two input symbols S1 and S2.
                                          A            1                    =                      [                                                                                s                    1                                                                                        s                    2                    *                                                                                                                    s                    2                                                                                        -                                          s                      1                      *                                                                                            ]                          ,                              A            2                    =                      [                                                                                s                    1                                                                                        s                    2                    *                                                                                                                    s                    2                                                                                        -                                          s                      1                      *                                                                                            ]                          ,                                  ⁢                              A            3                    =                      [                                                                                s                    1                                                                                        -                                          s                      2                      *                                                                                                                                        s                    2                                                                                        s                    1                    *                                                                        ]                          ,                              A            4                    =                      [                                                                                -                                          s                      1                                                                                                            s                    2                    *                                                                                                                    s                    2                                                                                        s                    1                    *                                                                        ]                                              (        4        )            
In the coding matrix as Equation (3), the number of rows corresponds to the number of transmit antennas and the number of columns represents time and frequency being needed to transmit three symbols. Here, first two columns are transmitted to frequency, f1, the other two columns are transmitted to frequency, f2. The front one of the two columns being transmitted through f1 is transmitted for a first time interval, t1, the rear column is transmitted for a second time interval, t2. Thus, four symbols are transmitted through three antennas for two time and frequency intervals.
As such context, data of the first two columns may be transmitted for t1, the other two columns, for t2. The front one of data of two columns being transmitted for t1 is transmitted for f1, and the rear data, for f2. That is, the first, second, third and fourth column data are transmitted for f1 and t1, f1 and t2, f2 and t1, and f2 and t2, respectively.
However, as described above, it is obvious not to be required to limit to use both time and frequency when signals are transmitted.
The each element for four columns uses the same frequency and can be transmitted having different time interval each other. That is, the first, second, third and fourth column data are transmitted for t1, t2, t3, and t4, respectively.
Also, all elements can be transmitted for the same time interval with different frequency region each other. That is, the first, second, third and fourth column data are transmitted for f1, f2, f3, and f4, respectively.
As described above, the STFBC coder 108 generates four symbol sequences using the input four symbols, their conjugates and negatives, and transmits them through the three antennas 110, 112, 114 for two time and frequency intervals. That is, the first, second, and third rows of space-time frequency block code configured in the STFBC coder 108 are transmitted through the first, second and third antennas 110 to 114, respectively. Because the symbol sequences for the respective antennas, that is, the columns of the coding matrix, are mutually orthogonal, as high a diversity gain as a diversity order is achieved.
As described above, the Alamouti STFBC technique offers the benefit of achieving as high a diversity order as the number of Tx antennas, namely a full diversity order, without sacrificing data rate by transmitting complex symbols through only two Tx antennas.
FIG. 2 is a block diagram of a receiver in the mobile communication system using the STFBC scheme. In particular, the receiver in FIG. 2 is the counterpart of the transmitter illustrated in FIG. 1.
As described above, the receiver includes a plurality of Rx antennas 200 to 202, a channel estimator 204, a signal combiner 206, a detector 208, a parallel-to-serial (P/S) converter 210, and a demodulator 212.
Referring to FIG. 2, the first to Pth Rx antennas 200 to 202 provide signals received from the three antennas of the transmitter illustrated in FIG. 1 to channel estimator 204 and the signal combiner 206. The channel estimator 204 estimates channel coefficients representing channel gains from the Tx antennas 106 to 112 to the Rx antennas 200 to 202 using the signals received from to Pth Rx antennas 200 to 202.
The signal combiner 206 combines the signals received from the Pth Rx antennas 200 to 202 with the channel coefficients from the channel estimator 204 in a predetermined method.
The detector 208 generates hypothesis symbols by multiplying the combined symbols by the channel coefficients, calculates decision statistics for all possible transmitted symbols from the transmitter using the hypothesis symbols, and detects the actual transmitted symbols through threshold detection.
The P/S converter 210 serializes the parallel symbols received from the detector 208, and the demodulator 212 demodulates the serial symbol sequence in a predetermined demodulation scheme, thereby recovering the original information bits.
In this manner, the use of STFBC encoding four symbols using Alamouti scheme with three antennas by Equation (3) enables linear decoding at the receiver, thereby decreasing decoding complexity. Here, Sundar Rajan group uses a fixed phase rotation angle ⊖, regardless of modulation scheme. That is, ⊖=(½)atan 2 is used regardless of QPSK and 16QAM modulation scheme.
Now to describe that the coding gain of the Sundar Rajan group's STBFC can be further improved, a design of a space-time frequency block code will be described below.
Two designs of a space-time trellis code were proposed in a paper by Tarokh in 1997. Before explaining the design rule, an error probability bound of the space-time trellis code is as follows.
                              p          ⁡                      (                          c              →              e                        )                          ≤                                            (                                                ∏                                      n                    =                    1                                    r                                ⁢                                                                  ⁢                                  λ                  n                                            )                                      -              M                                ⁢                                    (                                                E                  s                                                  4                  ⁢                                      N                    0                                                              )                                      -              rM                                                          (        5        )            
Equation (5) is an equation representing pairwise error probability of the space-time trellis code. In Equation (5), r donates a rank of a c−>e matrix, M denotes the number of Rx antennas, and λ denotes a diagonal term of the c−>e matrix. Es denotes symbol energy and N0 denotes noise. In a right-hand side of Equation (5), a first term is a determinant criterion representing a coding gain or coding advantage and a second term is a rank criterion representing a diversity gain.
1) Determinant Criterion: It is a design condition for maximizing coding gain and the product of λ1 . . . , λr should be designed to have the largest code in order to obtain the large coding gain.
2) Rank Criterion: It is a design condition for maximizing diversity gain and should be designed to have a full rank.
Regarding the coding gain, the Sundar Rajan group calculated ⊖ by applying the design rule 1) to the space-time block coding. This method is achieved by maximizing a minimum value among the products of Eigen values (not zero) of N*M matrices A(c, e) corresponding to this a difference (c−e) between two different signal vectors. If calculating ⊖ by this method, ⊖ is equal to about 59°.
FIG. 4 is a graph of a minimum coding gain obtained by the conventional design rule proposed by Tarokh while changing ⊖ from 0 to 90. As illustrated in FIG. 4, it can be seen that the minimum coding gain is greatest at a phase of 59°.
In an actual simulation, however, the use of this value degrades the system performance. For example, if a phase rotation angel ⊖ is calculated using the Tarokh's design rule, the phase rotation angle ⊖ is 59°. In this case, the minimum coding gain is 1.7659 and happens 2048 times when QPSK is assumed. The second smallest coding gain is 1.8779 and happens 1024 times. The third smallest coding gain is 3.5318 and happens 3072 times. The fourth smallest coding gain is 3.7558 and happens 768 times. If 63.43° is assumed, however, the minimum coding gain is 1.6002 and happens 2048 times. The second smallest coding gain is 2.3994 and happens 1024 times. The third smallest coding gain is 3.2001 and happens 3072 times. The fourth smallest coding gain is 4.000 and happens 3072 times. According to the design rule, compared with the two cases, the performance must be better in the use of 59° at which the coding gain is good. However, the performance is better in the use of 63.43
Accordingly, the design rule 1) is not perfect. That is, there is a need for a method of further improving the coding gain at the Sudar Rajan group's transmitter.